Question

Dr. Sherman is studying a bacterial colony with a population of 55,000 bacteria. The colony is growing 15% per hour. How many bacteria will the colony contain in 5 hours?If necessary, round your answer to the nearest whole number.

Answer 1

Given:

original population of the bacteria = 55 000

growth rate = 15% per hour

time = 5 hrs

The population after t hours can be calculated using the formula:

`\begin{gathered} P=P_Oe^(rt) \\ \text{Where P is the population after time t} \\ P_o\text{ is the original population} \\ r\text{ is the growth rate} \\ \text{and t is the time duration} \end{gathered}`

Substituting the given values into the formula, we have the population of the bacteria after 5 hrs to be:

`\begin{gathered} P\text{ = 55000}* e^(0.15*5) \\ =\text{ }116435.009 \end{gathered}`

Hence, the population of the bacteria after 5 hours is 116435 bacteria